Finite Group Databasebeta

?

← Prev (#7666394) Next (#7666396) →

C₂×#59466 #7666395

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(4,6)(8,9)(11,12,14,15)(13,17,18,16)(20,23)(25,26);(3,4,7,6)(5,9,10,8)(12,15)(16,17)(19,20,24,23)(21,25,22,26);(11,12)(13,16)(14,15)(17,18)(19,21,24,22)(20,25,23,26);(3,5,7,10)(4,8,6,9)(11,12)(13,16)(14,15)(17,18)(19,22,24,21)(20,26,23,25);(3,6,7,4)(5,9,10,8)(11,13,14,18)(12,16,15,17)(19,23,24,20)(21,26,22,25)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573591);